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Tag: Spin-Flip

One concept which exists in Science, is that certain theories are Falsifiable. This means that a given hypothesis will predict some sort of experimental outcome, which other theories would not predict, and then an experiment can be performed to test whether this outcome is according to the theory. If it is not, then this test will break the theory, and will thus falsify it.

Quantum Mechanics is often Falsifiable. If the reader thinks it is not, then maybe the reader is confusing Quantum Mechanics with String Theory, which is supposedly not falsifiable? And thinking that String Theory is just the same thing as Quantum-Mechanics, is a bit like thinking that Cosmology is just the same thing as Astronomy.

According to Quantum Mechanics, light can be polarized, just as it can according to the classical, wave-based theory of light. Only, because according to Quantum-Mechanics light is driven by particles – by photons – its explanation of polarization is quite different from polarized light, according to the classical, electrodynamic explanation.

According to wave-based light, plane-polarized light is the primary phenomenon, and circular-polarized light is secondary. Circular-polarized light would follow, when waves of light are polarized in two planes at right-angles to each other, but when these waves also have a 90⁰ phase-shift.

According to Quantum-Mechanics, the photon is in itself a circular-polarized quantum of light, of which there can trivially be left- and right-handed examples. According to Quantum-Mechanics, plane-polarized light forms, when left- and right-handed photons pair up, so that their electrostatic components form constructive interference in one plane, while canceling at right-angles to that plane.

From a thermodynamic point of view, there is little reason to doubt that photons could do this, since the particles which make up matter are always agitated, and since the photons in an original light-source also have some random basis. So a conventional plane-polarizing filter, of the kind that we used to attach to our film-cameras, would not be so hard to explain. It would just need to phase-shift the present left-handed photons in one way, while phase-shifting the present right-handed ones oppositely, until they line up.

But there exists one area in which the predictions of Quantum-Mechanics do not match those of classical wave-mechanics. If we are given a digital camera that accepts lens-attachments, we will want to attach circular polarizing filters, instead of plane-polarizing filters. And the classical explanation of what a circular polarizer does, is first to act as a plane-polarizer, which thereby selects a plane of polarization which we want our camera to be sensitive to, but the output of which is next circularly-polarized, so that light reaches the autofocus mechanism of the camera, which is still not plane-polarized. Apparently, fully plane-polarized light will cause the autofocus to fail.

This behavior of a polarizer is easily explained according to Quantum-Mechanics. The plane-polarized light which is at first admitted by our filter, already possesses left- and right-handed photons. After that, we could visualize sorting out the photons that are circular-polarized in the wrong direction.

But the opposite behavior of a filter would not be predicted by Quantum-Mechanics. According to that, if we first pass randomly-polarized light through a circular polarizer, and if we then pass the resulting beam into a plane-polarizer, we should not be able to obtain plane-polarized output from the last polarizer.

According to the classical explanation of light, this should still be an easy thing to do. Our circularly-polarized light is supposed to have two components at right-angles, and our plane-polarizer should only allow vibration in one plane. But according to Quantum-Mechanics, if the incident beam is already circularly-polarized, it should only consist of either left-handed or right-handed photons, and then a simple filter should not be able to conjure photons that are not present in the original beam. And so our circularly-polarized light should not be convertible into plane-polarized light.

Under ‘the term NMR’, people may correctly understand two different subjects:

Why do subatomic particles, in this case nuclei, precess?

How do Engineers exploit this precession, in order to form 2D and 3D images, in ‘NMRI’?

In this posting, I am only going to address subject (1).

Precession and spin are easier to understand, when we can simply apply the Newtonian concepts. Quantum Mechanics today tends to obscure the subject of precession. And so for most of this post, I am going to make the somewhat daft assumption that the precession of subatomic particles, is Newtonian.

If a gyroscope is spinning along an arbitrary axis, and if we apply torque to its axis, this torque integrates into the spin vector – at an angle to the existing spin vector. Unless we are accelerating or slowing down its spin. This results in the spin vector rotating – and thus in precession.

But, if we have seen the demonstration in which an off-axis gyroscope is precessing on a passive pedestal, we also observe that eventually the phenomenon weakens, and that the practical axis seems to shift further and further in the direction gravity is pulling on it.

The reason this weakening takes place, is the fact that some additional torque is being applied to the gyroscope, against the direction in which it is precessing. Otherwise, it would just precess forever. This additional torque could be due to friction with the pedestal, due to air resistance, due to magnetism, or whatever.

An artillery shell is aerodynamically designed, so that as long as it has excess spin, interaction with the air will always push it in the direction of any existing precession, and so this type of object will tend to straighten its axis of spin, into the direction with which it is flying. This would be the equivalent to the gyro from before, straightening up and standing up against gravity again.

Atomic nuclei that have an odd mass number, also have a non-zero spin quantum number, thus having spin, and also have a magnetic dipole moment. The wanton assumption could be made that its magnetic dipole moment is always parallel to its axis of spin. But then if we visualize matter as consisting of nuclei that are separated by vast, less-dense clouds of electrons, it would seem to follow that each nucleus is always precessing in response to local magnetic fields.

And even if we were to apply an external magnetic field to such a system, it would follow that precession could not yet be detected externally, because the nuclei are all out-of-phase. Ostensibly, they would also continue to precess, and to stay out of phase, simply due to an applied magnetic field. The only big difference with the practical gyro should then be, that the magnitude of their spin-vector should never change, since this should be intrinsic.

But if we were to insist on this very Newtonian description, then something else should also happen that is not as obvious. Those thin wisps of electrons should not only react to the applied field, but also locally, to the field of each nucleus precessing. So if we assume conservation of energy, there would also be reactive torque acting on each nucleus, in response to its own precession, because the density of the electron clouds is not zero.

After a certain settling period which is measurable, the nuclei end up aligning themselves with the applied field, resulting in the state that has its lowest-possible potential energy. This takes milliseconds instead of the nanoseconds that some of these behaviors should take on the subatomic scale. Precession has still not been detected.

Likewise, the fact that subatomic decay can take years instead of nanoseconds, refutes certain mundane explanations, of what might be causing that.

Well, one thing that Scientists can do is compute what the dipole moment of such a nucleus is, as well as the magnitude of its angular momentum – spin – and to compute as a function of the applied field-intensity, with what frequency all the nuclei should be precessing… This frequency is called the “Larmor Frequency”.